Question

Express each of the following ratios in simplest form:
(i) $24:40$
(ii) $13.5:15$
(iii) $6\frac{2}{3}:7\frac{1}{2}$
(iv) $\frac{1}{6}:\frac{1}{9}$
(v) $4:5:\frac{9}{2}$
(vi) $2.5:6.5:8$

Answer 1

(i)

$=\frac{24}{40}$

$=\frac{24÷8}{40÷8}$

$=\frac{3}{5}$

$=3:5$
Hence, $24:40$ in its simplest form is $3:5$.
(ii)

$13.5:15$

$=\frac{13.5}{15}$

$=\frac{13.5\times 10}{15\times 10}$

$=\frac{135}{150}$

$=\frac{135÷15}{150÷15}$

$=\frac{9}{10}$

$=9:10$

Hence, $13.5:15$ in its simplest form is $9:10$.
(iii)

$6\frac{2}{3}:7\frac{1}{2}$

$=\frac{20}{3}:\frac{15}{2}$

$=\frac{\frac{20}{3}}{\frac{15}{2}}$

$=\frac{20}{3}\times \frac{2}{15}$

$=\frac{4}{3}\times \frac{2}{3}$

$=\frac{8}{9}$

$=8:9$

Hence, the simplest form of $6\frac{2}{3}:7\frac{1}{2}=8:9$

(iv) 24:40

$\frac{1}{6}:\frac{1}{9}$

$=9 : 6$

$=\frac{9}{6}$

$=\frac{9÷3}{6÷3}$

$=\frac{3}{2}$

$=3:2$

Hence, the simplest form of $9:6$ is $3:2$

(v)

$4:5:\frac{9}{2}$

$=\frac{4}{1}:\frac{5}{1}:\frac{9}{2}$

$=\frac{4}{1}\times 2:\frac{5}{1}\times 2:\frac{9}{2}\times 2$

$=8:10:9$

Therefore, The simplest form of $4:5:\frac{9}{2}$ is $8:10:9$

(vi)

$2.5:6.5:8$

$=\frac{25}{10}:\frac{65}{10}:8$

$=\frac{25}{10}\times 10:\frac{65}{10}\times 10:8\times 10$

$=25:65:80$

$=25÷5:65÷5:80÷5$

$=5:13:16$

Hence, the simplest form of $2.5:6.5:8$ is $5:13:16$.